Adaptive Friction Compensation: Modular Design with Passive Identifier

For a second-order mechanical system incorporating Coulomb frictional effect, a nonlinear adaptive control that achieves a controller-identifier separation is designed. This modularity is made possible by the strong input-to-state stability ISS property of the ISS controller with respect to the parameter estimation error as input. This input is independently guaranteed to be bounded by the passive identifier. We use two types of passive identifiers: z-scheme passive identifier and x-scheme passive identifier. These designs are more flexible than the Lyapunov-based design and lead to lower control effort. In addition, the advantages and disadvantages of z-scheme and x-scheme are presented. Transient performance of the system is enhanced with a trajectory initialization technique. The validity and effectiveness of the proposed friction compensator is verified by simulation for position tracking control under the influence of Coulomb friction.